Beware of the average monsters

Sri Humana: So what are we going to discuss today.

Ann: I heard this interesting news that our per capita income is actually growing

Garret: Boring, I watched fascinating horror movie.

Sarah: And Emily is having nightmares and I haven’t slept all night.

Thomas: To tell you the truth I do not like horror movies. But from the ones I have seen the whole script is around some kind of a monster. All these horrible creatures rarely have something in common but they are rather unique. Now try this: suppose you got the Predator, the Alien, Godzilla, Dracula and Jason — how would the average monster look like — ohhhh it will be a rather funny and ridiculous.

Now in your everyday life you are been bombed with all kinds of average statistics. Journalists use them, politicians use them and your boss use them.

Average salary, average IQ, average results and of course the average person. The average person on earth is 1.8m tall, has 110 IQ, earns 5000\$ per year, have one and a half child, is half Chinese half Indian and is half man half woman. What a monster!!!

The most dangerous average monsters are the ones in areas where results are not equally distributed. These should be areas like wealth, Internet traffic, cities sizes, areas burned by fires and other social phenomena’s.

Do not get me wrong, average numbers have meaning but mostly when mentioned with things that are distributed normally like people height, IQ, health, school grades, sunny days and etc.

Consider a big sample of wealth of random people. No consider the same sample but with Bill Gates in it. How would the average wealth change?

Consider a big sample of random people’s IQ. No consider the same sample but with Einstein in it. How would the average IQ change?

There is this basic metric in statistics called standard deviation. It simply measures the deviation from the average number. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data points are spread out over a large range of values. If you are in the second scenario maybe your average number has no use.

Stop believing in some average monsters and your nightmares may go away.

Here are the 8 steps how you can calculate a standard deviation:

3. Calculate the average of your data by dividing the total to the number of records (980/7=140)
4. Subtract from each actual number the average number
5. Square the above numbers
6. Sum all squared numbers
7. Calculate the average of all the numbers in step 5
8. Square root step 7

The short way is to use STDEV function in a spreadsheet program.

So 35 is the standard deviation of your data which means you may anticipate your next observation to be 140 +- 35 (if your sample is representative).

Standard deviation is largely use metric and especially in evaluating risks. Many people fall in the trap of this metric as they become over confident about risk in domains which do have extreme distributions (this actually caused the financial crisis from 2008). So use standard deviation wisely and do not get over confident about it especially if you are in the social domain.

Some Questions for you: Do you consider yourself “an average person”? What is the average weather in Sahara Desert and in Chicago?

Originally published at Ivan Petkov.

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